Unfortunately, it will take time for the Trichlor to dissolve to give you the CYA you need. If you want to get CYA into the pool faster while adding chlorine at the same time, then you could use Dichlor powder/granular. For every 10 ppm Free Chlorine (FC) added by Dichlor, it also increases CYA by 9 ppm. So in 13,500 gallons that's about 7 pounds of Dichlor to get you to 30 ppm and about 11 pounds of Dichlor to get you to 50 ppm.
However, since you want to fight an algae bloom, I'd only add a smaller amount of CYA, say around 20 ppm, and then use chlorinating liquid or bleach to maintain the shock level of FC (see this chart). You'll need a lower chlorine level to fight the algae bloom this way and it will go a little faster.
After you clear you pool of algae, your can use more Dichlor or even Trichlor pucks or pure CYA at that point to keep adding to CYA.
Richard
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